c     Date: Fri, 4 Mar 1994 00:06:47 -0500
c     From: Netlib Reply Daemon <netlibd@netlib1.EPM.ORNL.GOV>
c     To: dima@esm.ph.flinders.edu.au
c     Subject: Re: send zgeco from linpack  1
cat > linpack/zgeco.f <<'CUT HERE............'
      subroutine zgeco(a,lda,n,ipvt,rcond,z)
      integer lda,n,ipvt(1)
      complex*16 a(lda,1),z(1)
      double precision rcond
c
c     zgeco factors a complex*16 matrix by gaussian elimination
c     and estimates the condition of the matrix.
c
c     if  rcond  is not needed, zgefa is slightly faster.
c     to solve  a*x = b , follow zgeco by zgesl.
c     to compute  inverse(a)*c , follow zgeco by zgesl.
c     to compute  determinant(a) , follow zgeco by zgedi.
c     to compute  inverse(a) , follow zgeco by zgedi.
c
c     on entry
c
c        a       complex*16(lda, n)
c                the matrix to be factored.
c
c        lda     integer
c                the leading dimension of the array  a .
c
c        n       integer
c                the order of the matrix  a .
c
c     on return
c
c        a       an upper triangular matrix and the multipliers
c                which were used to obtain it.
c                the factorization can be written  a = l*u  where
c                l  is a product of permutation and unit lower
c                triangular matrices and  u  is upper triangular.
c
c        ipvt    integer(n)
c                an integer vector of pivot indices.
c
c        rcond   double precision
c                an estimate of the reciprocal condition of  a .
c                for the system  a*x = b , relative perturbations
c                in  a  and  b  of size  epsilon  may cause
c                relative perturbations in  x  of size  epsilon/rcond .
c                if  rcond  is so small that the logical expression
c                           1.0 + rcond .eq. 1.0
c                is true, then  a  may be singular to working
c                precision.  in particular,  rcond  is zero  if
c                exact singularity is detected or the estimate
c                underflows.
c
c        z       complex*16(n)
c                a work vector whose contents are usually unimportant.
c                if  a  is close to a singular matrix, then  z  is
c                an approximate null vector in the sense that
c                norm(a*z) = rcond*norm(a)*norm(z) .
c
c     linpack. this version dated 08/14/78 .
c     cleve moler, university of new mexico, argonne national lab.
c
c     subroutines and functions
c
c     linpack zgefa
c     blas zaxpy,zdotc,zdscal,dzasum
c     fortran dabs,dmax1,dcmplx,dconjg
c
c     internal variables
c
      complex*16 zdotc,ek,t,wk,wkm
      double precision anorm,s,dzasum,sm,ynorm
      integer info,j,k,kb,kp1,l
c
      complex*16 zdum,zdum1,zdum2,csign1
      double precision cabs1
      double precision dreal,dimag
      complex*16 zdumr,zdumi
      dreal(zdumr) = zdumr
      dimag(zdumi) = (0.0d0,-1.0d0)*zdumi
      cabs1(zdum) = dabs(dreal(zdum)) + dabs(dimag(zdum))
      csign1(zdum1,zdum2) = cabs1(zdum1)*(zdum2/cabs1(zdum2))
c
c     compute 1-norm of a
c
      anorm = 0.0d0
      do 10 j = 1, n
         anorm = dmax1(anorm,dzasum(n,a(1,j),1))
   10 continue
c
c     factor
c
      call zgefa(a,lda,n,ipvt,info)
c
c     rcond = 1/(norm(a)*(estimate of norm(inverse(a)))) .
c     estimate = norm(z)/norm(y) where  a*z = y  and  ctrans(a)*y = e .
c     ctrans(a)  is the conjugate transpose of a .
c     the components of  e  are chosen to cause maximum local
c     growth in the elements of w  where  ctrans(u)*w = e .
c     the vectors are frequently rescaled to avoid overflow.
c
c     solve ctrans(u)*w = e
c
      ek = (1.0d0,0.0d0)
      do 20 j = 1, n
         z(j) = (0.0d0,0.0d0)
   20 continue
      do 100 k = 1, n
         if (cabs1(z(k)) .ne. 0.0d0) ek = csign1(ek,-z(k))
         if (cabs1(ek-z(k)) .le. cabs1(a(k,k))) go to 30
            s = cabs1(a(k,k))/cabs1(ek-z(k))
            call zdscal(n,s,z,1)
            ek = dcmplx(s,0.0d0)*ek
   30    continue
         wk = ek - z(k)
         wkm = -ek - z(k)
         s = cabs1(wk)
         sm = cabs1(wkm)
         if (cabs1(a(k,k)) .eq. 0.0d0) go to 40
            wk = wk/dconjg(a(k,k))
            wkm = wkm/dconjg(a(k,k))
         go to 50
   40    continue
            wk = (1.0d0,0.0d0)
            wkm = (1.0d0,0.0d0)
   50    continue
         kp1 = k + 1
         if (kp1 .gt. n) go to 90
            do 60 j = kp1, n
               sm = sm + cabs1(z(j)+wkm*dconjg(a(k,j)))
               z(j) = z(j) + wk*dconjg(a(k,j))
               s = s + cabs1(z(j))
   60       continue
            if (s .ge. sm) go to 80
               t = wkm - wk
               wk = wkm
               do 70 j = kp1, n
                  z(j) = z(j) + t*dconjg(a(k,j))
   70          continue
   80       continue
   90    continue
         z(k) = wk
  100 continue
      s = 1.0d0/dzasum(n,z,1)
      call zdscal(n,s,z,1)
c
c     solve ctrans(l)*y = w
c
      do 120 kb = 1, n
         k = n + 1 - kb
         if (k .lt. n) z(k) = z(k) + zdotc(n-k,a(k+1,k),1,z(k+1),1)
         if (cabs1(z(k)) .le. 1.0d0) go to 110
            s = 1.0d0/cabs1(z(k))
            call zdscal(n,s,z,1)
  110    continue
         l = ipvt(k)
         t = z(l)
         z(l) = z(k)
         z(k) = t
  120 continue
      s = 1.0d0/dzasum(n,z,1)
      call zdscal(n,s,z,1)
c
      ynorm = 1.0d0
c
c     solve l*v = y
c
      do 140 k = 1, n
         l = ipvt(k)
         t = z(l)
         z(l) = z(k)
         z(k) = t
         if (k .lt. n) call zaxpy(n-k,t,a(k+1,k),1,z(k+1),1)
         if (cabs1(z(k)) .le. 1.0d0) go to 130
            s = 1.0d0/cabs1(z(k))
            call zdscal(n,s,z,1)
            ynorm = s*ynorm
  130    continue
  140 continue
      s = 1.0d0/dzasum(n,z,1)
      call zdscal(n,s,z,1)
      ynorm = s*ynorm
c
c     solve  u*z = v
c
      do 160 kb = 1, n
         k = n + 1 - kb
         if (cabs1(z(k)) .le. cabs1(a(k,k))) go to 150
            s = cabs1(a(k,k))/cabs1(z(k))
            call zdscal(n,s,z,1)
            ynorm = s*ynorm
  150    continue
         if (cabs1(a(k,k)) .ne. 0.0d0) z(k) = z(k)/a(k,k)
         if (cabs1(a(k,k)) .eq. 0.0d0) z(k) = (1.0d0,0.0d0)
         t = -z(k)
         call zaxpy(k-1,t,a(1,k),1,z(1),1)
  160 continue
c     make znorm = 1.0
      s = 1.0d0/dzasum(n,z,1)
      call zdscal(n,s,z,1)
      ynorm = s*ynorm
c
      if (anorm .ne. 0.0d0) rcond = ynorm/anorm
      if (anorm .eq. 0.0d0) rcond = 0.0d0
      return
      end
CUT HERE............
cat > linpack/zgefa.f <<'CUT HERE............'
      subroutine zgefa(a,lda,n,ipvt,info)
      integer lda,n,ipvt(1),info
      complex*16 a(lda,1)
c
c     zgefa factors a complex*16 matrix by gaussian elimination.
c
c     zgefa is usually called by zgeco, but it can be called
c     directly with a saving in time if  rcond  is not needed.
c     (time for zgeco) = (1 + 9/n)*(time for zgefa) .
c
c     on entry
c
c        a       complex*16(lda, n)
c                the matrix to be factored.
c
c        lda     integer
c                the leading dimension of the array  a .
c
c        n       integer
c                the order of the matrix  a .
c
c     on return
c
c        a       an upper triangular matrix and the multipliers
c                which were used to obtain it.
c                the factorization can be written  a = l*u  where
c                l  is a product of permutation and unit lower
c                triangular matrices and  u  is upper triangular.
c
c        ipvt    integer(n)
c                an integer vector of pivot indices.
c
c        info    integer
c                = 0  normal value.
c                = k  if  u(k,k) .eq. 0.0 .  this is not an error
c                     condition for this subroutine, but it does
c                     indicate that zgesl or zgedi will divide by zero
c                     if called.  use  rcond  in zgeco for a reliable
c                     indication of singularity.
c
c     linpack. this version dated 08/14/78 .
c     cleve moler, university of new mexico, argonne national lab.
c
c     subroutines and functions
c
c     blas zaxpy,zscal,izamax
c     fortran dabs
c
c     internal variables
c
      complex*16 t
      integer izamax,j,k,kp1,l,nm1
c
      complex*16 zdum
      double precision cabs1
      double precision dreal,dimag
      complex*16 zdumr,zdumi
      dreal(zdumr) = zdumr
      dimag(zdumi) = (0.0d0,-1.0d0)*zdumi
      cabs1(zdum) = dabs(dreal(zdum)) + dabs(dimag(zdum))
c
c     gaussian elimination with partial pivoting
c
      info = 0
      nm1 = n - 1
      if (nm1 .lt. 1) go to 70
      do 60 k = 1, nm1
         kp1 = k + 1
c
c        find l = pivot index
c
         l = izamax(n-k+1,a(k,k),1) + k - 1
         ipvt(k) = l
c
c        zero pivot implies this column already triangularized
c
         if (cabs1(a(l,k)) .eq. 0.0d0) go to 40
c
c           interchange if necessary
c
            if (l .eq. k) go to 10
               t = a(l,k)
               a(l,k) = a(k,k)
               a(k,k) = t
   10       continue
c
c           compute multipliers
c
            t = -(1.0d0,0.0d0)/a(k,k)
            call zscal(n-k,t,a(k+1,k),1)
c
c           row elimination with column indexing
c
            do 30 j = kp1, n
               t = a(l,j)
               if (l .eq. k) go to 20
                  a(l,j) = a(k,j)
                  a(k,j) = t
   20          continue
               call zaxpy(n-k,t,a(k+1,k),1,a(k+1,j),1)
   30       continue
         go to 50
   40    continue
            info = k
   50    continue
   60 continue
   70 continue
      ipvt(n) = n
      if (cabs1(a(n,n)) .eq. 0.0d0) info = n
      return
      end
CUT HERE............
cat > blas/zaxpy.f <<'CUT HERE............'
      subroutine zaxpy(n,za,zx,incx,zy,incy)
c
c     constant times a vector plus a vector.
c     jack dongarra, 3/11/78.
c
      double complex zx(1),zy(1),za
      double precision dcabs1
      if(n.le.0)return
      if (dcabs1(za) .eq. 0.0d0) return
      if (incx.eq.1.and.incy.eq.1)go to 20
c
c        code for unequal increments or equal increments
c          not equal to 1
c
      ix = 1
      iy = 1
      if(incx.lt.0)ix = (-n+1)*incx + 1
      if(incy.lt.0)iy = (-n+1)*incy + 1
      do 10 i = 1,n
        zy(iy) = zy(iy) + za*zx(ix)
        ix = ix + incx
        iy = iy + incy
   10 continue
      return
c
c        code for both increments equal to 1
c
   20 do 30 i = 1,n
        zy(i) = zy(i) + za*zx(i)
   30 continue
      return
      end
CUT HERE............
cat > blas/zscal.f <<'CUT HERE............'
      subroutine  zscal(n,za,zx,incx)
c
c     scales a vector by a constant.
c     jack dongarra, 3/11/78.
c     modified 3/93 to return if incx .le. 0.
c
      double complex za,zx(1)
      integer i,incx,ix,n
c
      if( n.le.0 .or. incx.le.0 )return
      if(incx.eq.1)go to 20
c
c        code for increment not equal to 1
c
      ix = 1
      do 10 i = 1,n
        zx(ix) = za*zx(ix)
        ix = ix + incx
   10 continue
      return
c
c        code for increment equal to 1
c
   20 do 30 i = 1,n
        zx(i) = za*zx(i)
   30 continue
      return
      end
CUT HERE............
cat > blas/izamax.f <<'CUT HERE............'
      integer function izamax(n,zx,incx)
c
c     finds the index of element having max. absolute value.
c     jack dongarra, 1/15/85.
c     modified 3/93 to return if incx .le. 0.
c
      double complex zx(1)
      double precision smax
      integer i,incx,ix,n
      double precision dcabs1
c
      izamax = 0
      if( n.lt.1 .or. incx.le.0 )return
      izamax = 1
      if(n.eq.1)return
      if(incx.eq.1)go to 20
c
c        code for increment not equal to 1
c
      ix = 1
      smax = dcabs1(zx(1))
      ix = ix + incx
      do 10 i = 2,n
         if(dcabs1(zx(ix)).le.smax) go to 5
         izamax = i
         smax = dcabs1(zx(ix))
    5    ix = ix + incx
   10 continue
      return
c
c        code for increment equal to 1
c
   20 smax = dcabs1(zx(1))
      do 30 i = 2,n
         if(dcabs1(zx(i)).le.smax) go to 30
         izamax = i
         smax = dcabs1(zx(i))
   30 continue
      return
      end
CUT HERE............
cat > blas/zdotc.f <<'CUT HERE............'
      double complex function zdotc(n,zx,incx,zy,incy)
c
c     forms the dot product of a vector.
c     jack dongarra, 3/11/78.
c
      double complex zx(1),zy(1),ztemp
      ztemp = (0.0d0,0.0d0)
      zdotc = (0.0d0,0.0d0)
      if(n.le.0)return
      if(incx.eq.1.and.incy.eq.1)go to 20
c
c        code for unequal increments or equal increments
c          not equal to 1
c
      ix = 1
      iy = 1
      if(incx.lt.0)ix = (-n+1)*incx + 1
      if(incy.lt.0)iy = (-n+1)*incy + 1
      do 10 i = 1,n
        ztemp = ztemp + dconjg(zx(ix))*zy(iy)
        ix = ix + incx
        iy = iy + incy
   10 continue
      zdotc = ztemp
      return
c
c        code for both increments equal to 1
c
   20 do 30 i = 1,n
        ztemp = ztemp + dconjg(zx(i))*zy(i)
   30 continue
      zdotc = ztemp
      return
      end
CUT HERE............
cat > blas/zdscal.f <<'CUT HERE............'
      subroutine  zdscal(n,da,zx,incx)
c
c     scales a vector by a constant.
c     jack dongarra, 3/11/78.
c     modified 3/93 to return if incx .le. 0.
c
      double complex zx(1)
      double precision da
      integer i,incx,ix,n
c
      if( n.le.0 .or. incx.le.0 )return
      if(incx.eq.1)go to 20
c
c        code for increment not equal to 1
c
      ix = 1
      do 10 i = 1,n
        zx(ix) = dcmplx(da,0.0d0)*zx(ix)
        ix = ix + incx
   10 continue
      return
c
c        code for increment equal to 1
c
   20 do 30 i = 1,n
        zx(i) = dcmplx(da,0.0d0)*zx(i)
   30 continue
      return
      end
CUT HERE............
cat > blas/dzasum.f <<'CUT HERE............'
      double precision function dzasum(n,zx,incx)
c
c     takes the sum of the absolute values.
c     jack dongarra, 3/11/78.
c     modified 3/93 to return if incx .le. 0.
c
      double complex zx(1)
      double precision stemp,dcabs1
      integer i,incx,ix,n
c
      dzasum = 0.0d0
      stemp = 0.0d0
      if( n.le.0 .or. incx.le.0 )return
      if(incx.eq.1)go to 20
c
c        code for increment not equal to 1
c
      ix = 1
      do 10 i = 1,n
        stemp = stemp + dcabs1(zx(ix))
        ix = ix + incx
   10 continue
      dzasum = stemp
      return
c
c        code for increment equal to 1
c
   20 do 30 i = 1,n
        stemp = stemp + dcabs1(zx(i))
   30 continue
      dzasum = stemp
      return
      end
CUT HERE............
cat > linpack/dcabs1.f <<'CUT HERE............'
      double precision function dcabs1(z)
      double complex z,zz
      double precision t(2)
      equivalence (zz,t(1))
      zz = z
      dcabs1 = dabs(t(1)) + dabs(t(2))
      return
      end
CUT HERE............
